This paper addresses the restoration of three-dimensional (3D) objects affected by noise, distance, and degradation processes. Our contributions are twofold. First, we propose an innovative method for estimating Racah moments, enabling the extraction of discriminative features for 3D restoration. Unlike conventional approaches with fixed parameters, our method employs a polynomial parameterization of Racah moments, allowing dynamic adjustment that enhances both restoration accuracy and depth estimation when combined with \(H_{\infty}\) deconvolution filtering. Second, we establish a mathematical correlation between Racah-based descriptors and the Fornasini–Marchesini local state-space model under polytopic uncertainty. A robust deconvolution filter is then designed to guarantee asymptotic stability and a prescribed \(H_{\infty}\) performance. To simplify synthesis, free matrix variables are introduced, yielding tractable linear matrix inequality (LMI) conditions via parameter-dependent polynomial techniques. Compared to 3D Krawtchouk and Dual Hahn moments, the proposed approach achieves over 30% improvement in noise robustness across diverse 3D objects. For example, in filtering tasks on 3D chairs under Gaussian noise, the ETIR method reduces reconstruction error from 9000 (simple) and 450 (matrix) to just 20. Similar gains are observed for airplane and teddy models, with error dropping to about 22 versus 60 (Krawtchouk) and 50 (Dual Hahn) under Gaussian noise variance 0.1.
